Kinetic entropy for layer-averaged hydrostatic Navier-Stokes equations

Emmanuel Audusse (1) , Marie-Odile Bristeau (2) , Jacques Sainte-Marie (3, 4)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 ANGE - Numerical Analysis, Geophysics and Ecology
3 LJLL - Laboratoire Jacques-Louis Lions
4 Cerema Direction Centre-Est - Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement - Direction Centre-Est

We are interested in the numerical approximation of the hydrostatic free surface incompressible Navier-Stokes equations. By using a layer-averaged version of the equations, we are able to extend previous results obtained for shallow water system and to derive a vertically implicit horizontaly explicit finite volume kinetic scheme that ensures the positivity of the approximated water depth and a fully discrete energy inequality.

Mots clés: free surface flows; layer-averaged model; hydrostatic reconstruction; kinetic solver; finite volumes; IMEX scheme; discrete entropy inequality; Incompressible Euler and Navier-Stokes sytems

Domaines: Analyse numérique [math.NA]

Emmanuel Audusse, Marie-Odile Bristeau, Jacques Sainte-Marie. Kinetic entropy for layer-averaged hydrostatic Navier-Stokes equations. 2017. ⟨hal-01583511v1⟩